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3 years ago

10

Explain how you could get a formula for the volume of the glass.

1 answer:

harkovskaia [24]3 years ago

6 0

Answer:

Step-by-step explanation:

a. find the vertical height of the bowl of glass

b.calculate the volume of the bowl of each glass

c.find the height of the water

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

mamaluj [8]

Answer:

$x = 10$ . In other words, there number of girls is $10$ .

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

$\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}$ .

Rewrite to obtain:

$\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}$ .

For this question:

$\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}$ .

$\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}$ .

Therefore:

$\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}$ .

On the other hand, there are $(15 + x)$ boys and girls in total. Using the formula for average:

$\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}$ .

From the question, this average should be equal to $123$ . In other words:

$\displaystyle \frac{1875 + 120\, x}{15 + x} = 123$ .

Solve this equation for $x$ to obtain:

$1875 + 120\, x= 123\, (15 + x)$ .

$(123 - 120)\, x = 1875 - 123 \times 15$ .

$x = 10$ .

In other words, the number of girls here is $10$ .

5 0

3 years ago

Find an equation of the sphere which contains points A(1, 3, 2) and B(4, 3, 7) and the distance between A and B is equal to the

Marina86 [1]

Answer:

The answer is 8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2

Step-by-step explanation:

First we need to find diameter of the sphere. The distance point A and point B is:

$d=\sqrt{(4-1)^2+(3-3)^2+(7-2)^2} \\d=\sqrt{3^2+0^2+5^2} \\d=\sqrt{34} \\d=5.83$

d/2=r=2.92

radius of the sphere is 2.92 units

and the center of the sphere is:

C=((4+1)/2,(3+3)/2,(7+2)/2)

C=(2.5,3,4.5)

We can write the equation of the sphere as:

$r^2=(x-2.5)^2+(y-3)^2+(z-4.5)^2\\8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2$

4 0

3 years ago

A wall has been built with two pieces of sheetrock, a smaller one and a larger one. The length of the smaller one is stored in t

marishachu [46]

Answer:

The answer is: small+large.

Step-by-step explanation:

If the variable of the smaller sheetrock is stored in small:

var small.

And the variable of the larger sheetrock is stored in large:

var large.

The length of the wall will be the sum of the two pieces of sheetrock:

small+large

For example:

var small = 5;

var large = 10;

small+large = 5 + 10 = 15 is the length of the wall.

4 0

4 years ago

13.At the Finch School bake sale, donuts sell

aliina [53]

Answer:

c)

Step-by-step explanation:

create a system of equations:

d + m = 104

2d + 3m = 243

now use substitution method based on 'd = 104 - m'

2(104 - m) + 3m = 243

208 - 2m + 3m = 243

208 + m = 243

m = 35

So, 35 muffins and 69 donuts were sold.

This is 34 more donuts than muffins.

7 0

3 years ago

Hannah lost four points on a test and earned four points on an extra credit question what does the sum of 0 mean in the descript

Dominik [7]

Answer:

Is that it's not about the answers and the questions

5 0

3 years ago